CHAPTER 14 Kinetics of a particle:Work and Energy 14.1 The Work of a Force 1. Definition of Work A force does work in a particle only when the particle undergoes a displacement in the direction of the force. Here =force acts on the particle = - =displacement of the particle = =angle between and

Unit of Work (SI) 1 N*m=1 joule (J) 1 ft*lb= 2. Work of a Variable Force

3. Work of a Constant Force moving along a straight live 4. Work of a Weight (position) (displacement)

5. Work of a spring forces Consider a linear spring force (1) Work done on the spring (2)Work of a spring done on the particle A particle (or only) attached to a spring F.B.D of spring and particle spring force on the particle work of a spring on the particle is

14.2 Principle of Work and Energy (PWE) 1. P.W.E The particle’s initial kinetic energy plus the work done by all the forces acting on the particle as it moves from its initial to its final position is equal to the particle’s final kinetic energy. or Here kinetic energy Work done by forces. 2. Derivation external force Equation of motion of particle Initial frame

Work done on particle P by external force is (1)Applying the kinetic equation to the above equation yields (2)Integrate both sides to yield or

3. Remark (1) PWE represents an integrated form of equation of motion (2) PWE provides a convenient substitution for When solving kinetic problems involving force, velocity and displacement. Ex: From P.W.E we have

14.3 Principle of Wok and Energy for a System of Particles principle of Work and Energy for Particle =resultant external force on ith particle =resultant internal force on ith particle Since work and energy are scalars both work and kinetic energy applied to each particle of the system may be added together algebraically. So that or

Here =System’s initial kinetic energy =System’s final kinetic energy =Work done by all external and internal forces Note: (1),since the paths over which corresponding particles travel will be different. (2),if the particles are contained within the boundary of a translating rigid body, or particles connected by inextensible cables. (Non rigid Body) Elastic..plastic… (1) Rigid body (2)

14.4 Power and Efficiency 1. Power The amount of work per unit of time. or unit of power 2. Efficiency 效率

14.5 Conservative Forces and Potential Energy 1. Conservative force The force moves the particle form one point to another point to produce work which is independent of the path followed by the particle. (1) Work done by weight (2) Work done by the spring force on a particle Conservative force Spring force

2. Potential Energy 位能 A measure of the amount of work a conservation force will do when it moves from a given position to the datum or a reference plane. (1) Gravitational potential energy (2) Elastic Potential Energy always positive. The spring force has the capacity for always positive work on the particle. datum (y=positive upward) datum 推回基準作 的功 作負功 Unstretched datum pull push

3. Potential Function V The work done by conservation forces(W and Fs) in moving the particle from point to point Is Ex: datum (Unstretched position)

14.6 Conservation of Energy The principle of work and energy is rewritten as Work done by conservative forces Work done by nonconservative forces If, then Conservation of energy The sum of the particle’s kinetic and potential energy remains constant during the motion. Conservation of energy for a system of particles is end